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Register a new userWigner-Weyl calculus in Keldysh technique
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We discuss the non-equilibrium dynamics of condensed matter/quantum field systems in the framework of Keldysh technique. In order to deal with the inhomogeneous systems we use the Wigner-Weyl formalism. Unification of the mentioned two approaches is demonstrated on the example of Hall conductivity. We express Hall conductivity through the Wigner transformed two-point Greens functions. We demonstrate how this expression is reduced to the topological number in thermal equilibrium at zero temperature. At the same time both at finite temperature and out of equilibrium the topological invariance is lost. Moreover, Hall conductivity becomes sensitive to interaction corrections.
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We propose a new version of Wigner-Weyl calculus for tight-binding lattice models. It allows to express various physical quantities through Weyl symbols of operators and Greens functions. In particular, Hall conductivity in the presence of varying and arbitrarily strong magnetic field is represented using the proposed formalism as a topological invariant.
We generalize the classic calculations by Rytova and Keldysh of screened Coulomb interaction in semiconductor thin films to systems with anisotropic permittivity tensor. Explicit asymptotic expressions for electrostatic potential energy of interaction in the weakly anisotropic case are found in closed analytical form. The case of strong in-plane anisotropy, however, requires evaluation of the inverse Fourier transform of $1/(k+Ak_x^2+Bk_y^2)$, which, at present, remains unresolved.
It is generally believed that a Wigner Crystal in single layer graphene can not form because the magnitudes of the Coulomb interaction and the kinetic energy scale similarly with decreasing electron density. However, this scaling argument does not hold for the low energy states in bilayer graphene. We consider the formation of a Wigner Crystal in weakly doped bilayer graphene with an energy gap opened by a perpendicular electric field. We argue that in this system the formation of the Wigner Crystal is not only possible, but different phases of the crystal with very peculiar properties may exist here depending on the system parameters.
We present a detailed theoretical analysis of the Wigner crystal states in confined semiconducting carbon nanotubes. We show by robust scaling arguments as well as by detailed semi-microscopic calculations that the effective exchange interaction has an SU(4) symmetry, and can reach values even as large as $Jsim 100 {rm ,K}$ in weakly screened, small diameter nanotubes, close to the Wigner crystal - electron liquid crossover. Modeling the nanotube carefully and analyzing the magnetic structure of the inhomogeneous electron crystal, we recover the experimentally observed phase boundaries of Deshpande and Bockrath [V. V. Deshpande and M. Bockrath, Nature Physics $mathbf 4$, 314 (2008)]. Spin-orbit coupling only slightly modifies these phase boundaries, but breaks the spin symmetry down to SU(2)$times$SU(2), and in Wigner molecules it gives rise to interesting excitation spectra, reflecting the underlying SU(4) as well as the residual SU(2)$times$SU(2) symmetries.
Distinct to type-I Weyl semimetals (WSMs) that host quasiparticles described by the Weyl equation, the energy dispersion of quasiparticles in type-II WSMs violates Lorentz invariance and the Weyl cones in the momentum space are tilted. Since it was proposed that type-II Weyl fermions could emerge from (W,Mo)Te2 and (W,Mo)P2 families of materials, a large numbers of experiments have been dedicated to unveil the possible manifestation of type-II WSM, e.g. the surface-state Fermi arcs. However, the interpretations of the experimental results are very controversial. Here, using angle-resolved photoemission spectroscopy supported by the first-principles calculations, we probe the tilted Weyl cone bands in the bulk electronic structure of WP2 directly, which are at the origin of Fermi arcs at the surfaces and transport properties related to the chiral anomaly in type-II WSMs. Our results ascertain that due to the spin-orbit coupling the Weyl nodes originate from the splitting of 4-fold degenerate band-crossing points with Chern numbers C = $pm$2 induced by the crystal symmetries of WP2, which is unique among all the discovered WSMs. Our finding also provides a guiding line to observe the chiral anomaly which could manifest in novel transport properties.
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